I have always been interested in the Great
Pyramid and all of the funny and curious things it is supposed to be showing in
a geometrical way. I have read many books and magazines about, and so far I
have been satisfied with this, assuming that the facts that were told in were
correct and double-checked. But suddenly one amazing thing came to my mind: it
is vastly said that numbers π and Φ (the golden
number) are in the Pyramid. Well, if they were in two
independent parts of it, I would have been happy with that...but
they are not!The Pyramid is a geometrical figure whose dimensions
follow certain mathematical rules and relationships.(see http://www.omsi.edu/teachers/schools/portland/winterhaven/pyramids/
). For instance, the base of each side’s triangle is equal to the length of
this side. Hence, the distance from the centre to the middle point of any of
the sides equals half of the length of the side. This can be seen on this
figure:

This figureshows that Φis in the pyramid of Cheops. It is also known that the heigth is related
to the base perimetre in a factor of 2π.. (taken from Jim Loy’s page http://www.jimloy.com/pseudo/pyramid.htm and slightly modified)

Then, the base of the triangle shown in purple is related to the size of the sides of
the Pyramid. This triangle is were Φ is supposed to be
found:

In the Great Pyramid, the ratio between the length of the apothem and
the distance from the centre is Φ.

And this
triangle is a right triangle. So, the height, the side and the
hypotenuse must follow Pythagoras’ rule: L2 = x2 + y2.
One more relationship between these values.

It is also said that π is found in the Pyramid as:

In the Great Pyramid, the ratio between the total perimetre of the base
and the height is π.

So, there comes another dependency regarding
the side (the perimetre is the sum of the four sides) and the height.

From a mathematical point of view, we have two
variables (height and side) that depend on twoformulae...and Pythagoras’ theorem.

Are π and Φ then related?
That is the question I made to myself, because it does not make any sense!

That is why I am currently doing this study.

2)Building a triangle that hasπ and Φ, somehow:

In a right triangle like this,H2
= h2 + L2, as usual. If we want h and H
to be somehow proportional to L (or if somebody wanted so), let:

h = αL and H = βL

That eventually yields to:α2 = β2 + 1

Now, if somebody wanted (long ago!) to
have αand βset to something special, we should simply replace these variables
with the desired values, and check if the result is true.

For instance,

2 π h = 8Lóα = 4 / π

and (why not?) β = Φ = (1 + sqrt(5))/2

That yields:

Φ 2 = 16 / π 2 + 1

And given that Φ is a very nice number, and has the following property: Φ 2 = Φ +1

We have:

Φ≈ 16 / π 2

Or:

Sqrt
(Φ)*π≈ 4

Isn’t that funny?

I have computed (with Linux C) the value of Sqrt(Φ)*πand I got 3.9961675861352627291 (which is NOT 4, but it looks very
much like!)

I guess the error comes from assuming it is a
right triangle.

So, instead of doing reverse engineering (what
actually friends ofpaleoufology do) I
decided to design this non-right triangle using TurboCad (some free CAD
programme) with a standarized L = 1. As you can see on the picture, a
nice modern programme has the same errors than the pyramid: it makes a right
triangle! And, by the way, with the famous angle of 51,8º...

Anyway,
3.9961675861352627291 was, is and will always be different than 4.

If we
solve instead mathematically the intersection of those two
circles, so we may be as much accurate as we’d wish to be, let the first circle
(of radius Φ) be
centered at (0,0) and the second (radius = 4 / π ) at (1,0). Hence,

Please
take careful note that my goals and aims in this study have nothing to do with
other people’s, especially above’s mentioned T. Nevin, from whose web pages I simply
borrowed the information I needed, not the ideas.
So, I am nor for nor against any other
internet-published study about.)

These are
the actual dimensions of the Pyramid of Cheops:

This
second and third figures show how the base of the Pyramid is not a
square, but some kind of 4-pointed star.

As well
as this photo, taken from a plane on 1940:

Using
TurboCad I have drawn the base of the pyramid, using above’s values (note that DIRECTIONS
are meant CLOCKWISE, rather than the way the standards suggest:
otherwise East would be at the left of North!).

For
making this picture I simply drew the lines ndtc,
wdtc, edtc and stdc with
their corresponding lenghts and angles. Then I made the circle centered at the
top of ndtc with radius ln,
and the circle centered at the right of edtc
with radius re. Obviously, their intersection is the North-East corner.
And so forth for the remaining corners...

The resulting values for nw, ne, sw and se
segments match data provided by above’s figure, so I can assume I did
not make any mistake or misunderstanding.

DIRECTIONS:

This
figure shows the calculated DIRECTIONS for the
N, W, S and E lines (from East):

Comparing
to the ones taken from the web, which are relative to North and clockwise:

Ndtc =90º - (359,9586º - 360º) =90,0414º

Edtc =89,9083º + 270º = 359,9083º

Sdtc =179,9673º - 90º = 89,9673º

Wdtc =90º - (269,9587º - 360º) =180,0413º

This
figure shows the calculated DIRECTIONS for the NW,
NE, SE and SW lines (from East):